Interpretive Summary: Stepped chutes, often designed as stepped spillways dams, is a growing trend for rehabilitating aging embankment dams and the design for new dams. The chute steps may create a white water effect on the water surface due to air present in the water. This white water occurs when the chute is long enough for the air to become entrained in the flow. To examine the effect of design features including step height and chute slope on the development of air entrained flow, a multi-year research study at the United States Department of Agriculture (USDA)-Agricultural Research Service (ARS) was conducted. This study led to an extensively, broad dataset. Equations for air concentration and flow depth that are based on the step height, slope, and the location of where the air is first visible across the full width of the chute were developed. These equations provide advancements in practical design guidance for the training walls of the stepped chutes applied to new and aging embankment dams.

Technical Abstract:
Numerous contributions have been made on the hydraulic properties of the air entrainment inception point and aerated flow region especially for steep, stepped chutes. Stepped chutes applied to aging embankment dams to address inadequate spillway capacity and to provide overtopping protection is a growing trend. In many of these cases, the chute length is not sufficient to develop a fully aerated flow regime. For those chutes developing full aeration in the flow, flow bulking, an increase in flow depth due to air in the flow, occurs. A multi-year, large-scale research study at the USDA-Agricultural Research Service Hydraulic Engineering Research Unit, was conducted to evaluate the effect of step height (h) and slope on the air entrainment inception point, clear water flow depth, air concentration, and the bulked flow depth. This study led to an extensive dataset unmatched by previous studies due to sheer size of the testing facility and flow capacity to the model. Optimized empirical relationships for determining flow depth at any point along the chute, and new air concentration relationships for downstream of the inception point are provided. Analysis of the data indicates that the air concentration in the fully developed flow region is a function of the normalized h to critical depth, dc, and slope. The flow depth in the developing flow region is a function of h/dc, slope and the normalized length from the crest, L/Li. Flow depth in the fully developed flow region may be characterized by slope and h/dc. The results from this study are within plus/minus 10% error. The relationships provide advancements to practical design guidelines for the training walls of stepped chutes applied to new and aging embankment dams.